Method and Apparatus for Magnetic Contactless Measurement of Angular and Linear Positions

ABSTRACT

Contactless measurement of angular or linear positions is obtained by means of magnetic circuit configurations, biased by a permanent magnet, characterised by two airgaps whose relative geometry is designed to result in magnetic field values whose ratio is a function of the position to be measured. The magnetic field in said airgaps is measured by magnetic field probes, whose output signals are then electronically conditioned to generate a voltage proportional to said ratio. The output signal being function of a ratio, it naturally becomes insensitive to drifts of the magnet working point, or drifts in sensitivity of the magnetic field probes. In one embodiment said ratio of magnetic field values becomes a function of the relative angular displacement of two coaxial shafts, while becoming completely independent from their absolute angular displacement, allowing hence the realisation of simple and robust torque sensors.

This invention describes a method, and various apparatuses implementing said method, for the contactless measurement of angular and linear positions by means of magnetic fields.

Several devices are commercially available which already feature similar functions, although obtained by other means. A typical approach would consist in placing a magnetic field sensor in an airgap whose geometry changes as a function of the angular or linear displacement to be measured. Said change of geometry is arranged as to result in a corresponding change in the value of the magnetic field, B, as measured by said magnetic field sensor.

The change in the B field value can be obtained by either varying the length of the airgap, or its cross-section, or both, as a function of the displacement in position. The straight implementation of such basic approaches is rather obvious, being just a matter to devise magnetic circuit configurations such that the value of B is a direct function of the relative position of the composing parts. The simplest and most robust way to generate the required magnetic field would then make use of permanent magnets. Unfortunately things are not that straightforward, as the working point of low cost permanent magnets (PMs) is heavily affected by temperature, by naturally occurring demagnetization effects, and variations in magnetic circuit's total reluctance. To counteract the inaccuracies inherent to said trivial implementations, more sophisticated techniques have been developed, as disclosed in numerous patents.

In particular, EP 0 768 541 A1 (referred to as D1), “Capteur Magnétique de Position”, SAGEM SA, 01.10.1997, discloses a magnetic circuit configuration arranged as to generate two magnetic fields, B1 in airgap 1, and B2 in airgap 2, each one of which is a linear function of position, and whose sum is a constant value. The position is then measured by computing the value of the relative differential measurement (B1−B2)/(B1+B2), greatly reducing sensitivity to variations in temperature.

For magnetic type of contactless position measurements an additional source of inaccuracy are external stray fields, it is hence important to try to minimise their relative importance. U.S. Pat. No. 5,789,917 A1 (referred to as D2), “Magnetic Position Sensor with Hall Probe Formed in an Air Gap of a Stator”, Moving Magnet Technologies SA, Aug. 4, 1998, discloses a magnetic circuit configuration arranged as to effectively screen from external fields.

For the measurement of the value of the magnetic field, both D1 and D2 make use of Hall effect probes. Hall effect probes generate an output voltage, Vh (Volts), proportional to the value of the biasing current, Ib (Amperes), and to the magnetic field, B (Tesla), through the factor of proportionality, Kh (sensitivity, with units V/AT):

Vh=Kh*Ib*B  (1)

The method and apparatuses described in the following description make use of Hall probes for the measurement of B field values, however, the use of magnetoresitive type of sensors is also possible. Most commercially available magnetoresitive sensors are of the Wheatstone bridge type, generating an output voltage, Vm (mVolts), proportional to the value of the biasing voltage,Vb (Volts), and of the magnetic field, B (Tesla), through the factor of proportionality, Km (sensitivity, with units (mV/V)/(kA/m)):

Vm=Km*Vb*B  (2)

It shall be remarked that at the present state of the art most commercially available magnetoresitive bridge sensors are optimised for the measurement of relatively low B field values (few tens of mT), whereas Hall effect probes are better at the measurement of higher B field values (few hundreds mT). As the magnetic circuit configurations herewith described can easily achieve airgap B field values of few hundreds mT, and hence decreasing the relative importance of inaccuracies introduced by external stray fields, preference will be given to the use of Hall effect probes. In case it might turn out that for some applications also magnetorestive sensors becomes interesting, or that suitable magnetoresistive sensors might become commercially available, those skilled in the art can then easily imagine obvious way to replace said Hall probes with said magnetoresistive sensors.

Differently from the method disclosed in D1, which is based on the differential relative measurement (B1−B2)/(B1+B2), the method and apparatuses detailed in the following description make use of magnetic circuit configurations arranged in ways that the measurement of position corresponds to the simple ratio, B1/B2, between the B field values measured by two separate sensors, located in two separate airgaps. If said B1/B2 ratio is furthermore made dependent on geometric relationships only, then drifts of the PM's working point would automatically cancel out (appearing both at numerator and denominator). To achieve this result two basic magnetic circuit configurations are possible: parallel configuration, series configuration.

FIG. 1 a schematically depicts an example of parallel configuration, and whose relevant cross-section is displayed in FIG. 1 b.

It can be readily verified that said F the PM's Magnetomotive Force at any particular working point, the two parallel branches will experience magnetic fluxes φ1 and φ2, defined respectively by φ1=F/R1 and φ2=F/R2, where R1 and R2 are the respective reluctances (largely dominated by the length of the respective airgaps). Considering that B=φ/S, the voltage values generated by the Hall probes H1 and H2 are respectively:

Vh1=Kh1*Ib*F/(R1*S1) Vh2=Kh2*Ib*F/(R2*S2)  (3)

where S1 and S2 are the effective areas (effective areas are computed taking into account also border effects) of the airgap cross-sections coplanar with the respective Hall probes. If both Hall sensors are serially supplied with the same biasing current Ib (or magnetoresitive bridges are parallel supplied by the same biasing voltage Vb), by taking the ratio between the two Hall voltages, we finally have:

Vh1/Vh2=Kh1/Kh2*B1/B2=Kh1/Kh2*R2/R1*S2/S1  (4)

i.e.: a value which is completely independent from the value of the Magnetomotive Force F corresponding to that particular working point. It shall be noted that Kh1/Kh2 is explicitly maintained in the above expression, as Hall effect sensors of the same type (such as for example the KSY14 from Infineon) might differ in their sensitivity value. Hence, allowance for individual calibrations shall be foreseen, for example to be carried out during manufacturing by adjusting the gain of a pre-amplifier, or by means of simple resistive networks selected on test.

Furthermore, dependence from sensitivity through the ratio Kh1/Kh2 implies that a large part of the dependence on temperature of the sensitivity is also inherently compensated, the ratio of the two sensitivities being much less dependent on temperature than each of the sensitivities taken individually. The same considerations apply to any long-term effect resulting in degradation of sensitivity with time, such as for example total radiation dose, aging effects, and the like, provided that H1 and H2 are sensors of the same type (generally, sensors of the same type degrade the same way). Therefore, by choosing the same type of sensor for both H1 and H2, the ratio Kh1/Kh2 can be approximated by a constant value, const, largely independent from temperature and degradation effects, and equal to 1 for the ideal case Kh1=Kh2 corresponding to matched sensors, hence:

Vh1/Vh2=const*B1/B2=const*R2S2/R1S1  (5)

Making it explicit that the measurement of position, obtained by computing the ratio Vh1//Vh2, is a function of geometric relationships only, as represented by the ratio R2S2/R1S1. In FIG. 1 a, D is a ring of ferromagnetic material, whose thickness varies along its circumference. In this way, by rotating the ring relatively to the magnetic circuit, the total length of airgap 2 will vary, and consequently also the value of R2, as a function of the angle of rotation θ. The cross-section example depicted in FIG. 1 b schematically represents the equivalent magnetic circuit when ring D is rotated to an angular position corresponding to its maximum thickness being located in airgap 2. By suitably machining said ring D (carefully taking into account also the so called “border effects”) it is then possible to obtain an output signal Vh1/Vh2, which is a function of the rotation angle θ. The present invention is not concerned with the particular shape of ring D, as several different shapes may exist, but that all yield the same form for the output function. Let us take the example of an application for which a triangle output signal is required, the corresponding R2S2/R1S1 ratio can be obtained in several different ways:

-   -   a) by holding constant the geometry of airgap 1, so that the         product R1S1 is also constant, and by linearly increasing the         thickness of ring D between 0 and 180°, while its width is held         constant, to then linearly decrease it between 180° and 360° (of         course, introducing corrections to compensate for border         effects), the product R2S2 will be a linear function of θ;     -   b) as above, but holding constant the thickness of the ring, to         then vary its width;     -   c) any suitable combination of a) and b)     -   d) it is also possible to add a second ring, concentric to the         first one and passing through airgap 1, so that now the ratio         R2S2/R1S1 can be modulated by varying the geometry of both         airgap 1 and airgap 2 at the same time, as to obtain the desired         triangle form for the output function.

The cross-section schematically represented in FIG. 1 c represents instead an example of series configuration, whereby both airgaps see the same magnetic flux φ (provided that the magnetic circuit is arranged as to reduce leakage flux to negligible values). In such case ring D is shaped as to concentrate φ into a smaller area at the cross-section coplanar with sensor H2. In this way the B value measured by H2, B2=φ/S2, is larger than the one measured by H1, B1=φ/S1. For a series configuration it will hence be:

Vh1/Vh2=const*B1/B2=const*S2/S1  (6)

Therefore, also in this case the ratio Vh1/Vh2 is a function of geometric relationships only. By properly machining ring D, so that the ratio S2/S1 is a suitable function of angular position, it is then possible to obtain the desired form for the output function.

FIG. 1 d depicts one more example of series configuration, whereby ring D features a C shaped cross-section, whose parameters vary along the circumference as to obtain a S2/S1 ratio with the desired dependency from angular position.

Demonstrated that Vh1/Vh2 can be made to be function of geometric parameters only, through the ratio B1/B2=R2S2/R1S1 for the parallel configuration, and the ratio B1/B2=S1/S2 for the series configuration, in the following we will more simply refer to the “B1/B2 Ratio”, making it implicit that it will always be possible to identify a geometric configuration such that said “B1/B2 Ratio” is a suitable function of the position coordinate to be measured. For some applications, an output signal which is a linear function θ is preferred, and which might take the form of a triangle function, such as the example of FIG. 1 f (for this example the signal conditioning electronics generate an output signal linearly varying between 1V and 3V), or a of a saw tooth function. For some other applications, an output signal which is a sinus function of θ could instead be preferred. Each particular choice for the form of the output function has its own set of advantages and drawbacks, and which are already well known. Those skilled in the art would then choose the type of function that best suits a particular application.

It can additionally be remarked that choosing functions of the sinus or triangle form implies that the output signal at angle θ would be identical to the value of the output signal at θ+180°. To resolve such ambiguity a second magnetic circuit could be located 90° further along ring D. In this way, for the applications requiring a triangle function output a second 90° phase shifted triangle signal would be available. For the applications requiring an output sine function, the 90° phase shifted signal would coincide with a cosine function, so that industry standard SIN-COS type of output signals can be obtained.

For the magnetic circuit configurations depicted in FIGS. 1 a to 1 d, the only moving part is ring D, whereas the permanent magnet and the Hall probes are held in fixed positions. It is also possible to devise configurations characterised in that only the Hall probes are held in fixed positions, while the permanent magnet and the magnetic circuit are all part of a rotating assembly. An example of said rotating assembly is shown in FIG. 2 a, depicting a perspective view of a cross-section (non-magnetic spacers utilised to fix the two central rings to the shaft are omitted for clarity), and for which FIG. 2 b schematically represents the same cross-section. PM is an axially magnetised ring magnet, and D1 a to D2 b four rings of ferromagnetic material whose geometric parameters vary along the circumference. The magnetic circuit is then closed via the central shaft, also made of ferromagnetic material (alternatively, the magnetic circuit may also be closed via a tube, made of ferromagnetic material, surrounding said shaft). Said rings of ferromagnetic material are then arranged as to obtain a “B1/B2 Ratio” function of the angular position θ. Also for this type of rotating magnetic assembly solution the present invention is not concerned with the particular shapes that rings D1 a to D2 b might take, as several different shapes may exist, but that all yield the same form for the output function. It is for example possible to held constant the geometry of the airgap defined by D1 a and D1 b (or D2 a and D2 b), and vary the geometry of the other airgap, defined by D2 a and D2 b (or D1 a and D1 b), in a suitable way as to obtain a “B1/B2 Ratio” corresponding to the desired function of θ. Alternatively, it is also possible to obtain the desired dependence on θ, of the “B1/B2 Ratio”, by varying in suitable ways the geometry of both airgaps, instead of just one.

FIG. 2 c depicts a configuration similar to the one of FIG. 2 b, but where the two circular airgaps are located on opposite sides of the ring magnet.

For the configuration of FIG. 2 d the permanent magnet is instead a cylindrical bar placed along the central shaft. Said bar may also be of a hollow type, surrounding a central shaft made of a material, which, in such case, would not be ferromagnetic.

FIGS. 2 e and 2 f depict configurations characterised in that the permanent magnet is magnetised along the radial direction.

All of the magnetic circuit configurations described above refer to the measurement of angular positions. For those skilled in the art it is a trivial task to convert said configurations to the measurement of linear positions: just ideally cut all of the ring shaped components along one radius and ideally straighten them. The resulting straighten configurations are then suitable for the measurement of linear displacements.

In order to obtain an electrical signal proportional to the “B1/B2 Ratio” it is then necessary to implement some sort of electronic signal processing. FIG. 3 a schematically represents an example of signal processing chain:

-   -   H1 and H2 are two linear Hall effect probes, such as for example         Infineon's KSY14.     -   S is used to serially supply H1 and H2 with the same biasing         current, Ib, and hence preference would be given to a current         source, although a stable voltage source would also be suitable         (as variations in biasing current are automatically compensated         for when computing the ratio Vh1/Vh2 of the two signals).     -   SC represents a Signal Conditioning network, for example of the         passive or active types as usually suggested in the applications         notes of the sensor manufacturers, and which is necessary in         order to compensate for the inherent offset voltage of the Hall         probes, as well as to calibrate for any residual mismatch of         their respective sensitivities.     -   The generated Hall voltages, Vh1 and Vh2, are then fed to a         divider circuit, which might be chosen among the many well-known         analogue or digital types, to finally generate an output signal         proportional to the “B1/B2 Ratio”.

FIG. 3 b schematically depicts a signal processing chain suitable for magnetoresistive bridge type of sensors (MR1 and MR2). For most commercially available magnetoresistive bridges, the output signals, Vm1 and Vm2, are proportional to the supply voltage, rather than to the biasing current. Hence, in such case S would be a voltage source, used to parallel supply both magnetoresistive bridges.

It shall now be remarked that Hall effect and magnetoresistive sensors have recently become commercially available that include said Signal Conditioning circuitry, SC, co-packaged with the sensor itself. In particular, referring to integrated sensors of the Hall effect type, the integrated signal conditioning is usually arranged as to generate an output signal that is proportional to the supply voltage (examples are Infineon's TLE499x type of ratiometric linear Hall sensors), rather than to the supply current. Said type of ratiometric linear Hall sensors would therefore need to be parallel supplied, in the same way as already indicated in FIG. 3 b for magnetoresistive bridge type of sensors.

The signal conditioning chains schematically represented in FIGS. 3 a and 3 b both make use of a divider circuit to generate an output voltage proportional to the “B1/B2 Ratio”. Said divider circuit can be implemented using any of the commercially available divider integrated circuits, or it can also be implemented by means of digital techniques, such as for example a conventional microcontroller implementing an analogue to digital conversion followed by the actual computation of the ratio between the two digital values so obtained. In case required by the application, the digital quotient obtained could then be converted back to the analog domain by means of digital to analog conversion.

Alternatively, a simpler and very convenient way to generate such an output voltage is schematically represented in FIG. 3 c:

-   -   A feedback loop compares the output of one of the sensor, for         example Vh2, with a reference voltage Vref;     -   The error voltage, Vref-Vh2, is then used to proportionally         regulate the voltage controlled source S (whether it be of a         current or voltage source type), aiming to obtain a steady state         condition characterised in that Vref=Vh2, and resulting hence in         a steady state value for the biasing current defined by         Ib=Vref/(Kh2*B2)

Hence, thanks to said feedback loop, the output of the other sensor, v_(o) , will directly yield a voltage proportional to the “B1/B2 Ratio”:

v _(o)=Kh1/Kh2*Vref*B1/B2=Vref*B1/N2  (7)

Note that Kh1/Kh2=1 (as assumed in FIG. 3 c) only for the ideal case of sensors with matched, or calibrated, sensitivities. Incidentally, equation 7 suggests that by adjusting Vref, for example during factory calibration, it is possible to finely calibrate against any inherent mismatch between the sensitivities of the two sensors, while defining at the same time the overall gain of the sensor. The feedback loop depicted in FIG. 3 c, whereby the two Hall probes are connected in series, is ideally suited for simple linear Hall effect probes, such as for example the KSY14 from Infineon.

The feedback loop depicted in FIG. 3 d, whereby the two sensors are connected in parallel, is instead better suited for magnetoresistive bridge sensors as well as for ratiometric linear Hall sensors, such as for example the already mentioned Infineon's TLE499x types.

With reference to the sensor configurations described above, it can be remarked that from a manufacturing point of view it turns out very convenient to design the geometries of the two airgaps in such a way that:

-   -   One of the two airgaps is designed to result in a B value         reproducing the desired function of angular position, and which         we will call Variable Airgap.     -   The other airgap is designed to result in a B value as uniform         as possible along the circumference spanning the required range         of angular positions, and which we will call Reference Airgap.

Referring to FIGS. 3 c and 3 d, best accuracy can be achieved when sensor H2 (or MR2) is placed in the Reference Airgap, whereas sensor H1 (or MR1) is placed in the Variable Airgap. For output functions symmetrical with respect to 180° , such as for example triangle or sinus functions, the mechanical design can further be simplified by suppressing the Reference Airgap, and replacing it with a Virtual Reference Airgap built as follows:

-   -   the magnetic field sensor that was located in the Reference         Airgap is now moved to the Variable Airgap, but at a position         diametrically opposed (i.e.:180°) to the other sensor.     -   The mean of the B values measured by the two sensors, (B1+B2)/2,         is a constant independent from angular position, which can then         be used as a Virtual Reference Airgap functionally equivalent to         the former Reference Airgap.

FIG. 3 e depicts a signal conditioning and processing circuitry suitable for the Virtual Reference Airgap approach. A signal proportional to the magnetic field measured in the Virtual Reference Airgap, Bvirtual, is obtained by adding, and then dividing by two, the signals from the two magnetic field sensors, now located in the same airgap, at diametrically opposed angular positions. The skill in the art would typically realise such (Vh1+Vh2)/2 function by means of an operational amplifier in a conventional adder configuration. As in FIG. 3 c (3 d), the feedback loop will then react to held (Vh1+Vh2)/2 (i.e.: Bvirtual) at a constant value determined by Vref. Similar considerations apply when using magnetic field probes ratiometric with respect to the supply voltage, in which case H1 and H2 will be supplied in parallel rather than in series (as it was instead the case for FIG. 3 e).

For all purposes of compensating against temperature and aging drifts of magnet and magnetic field sensors characteristics, such a feedback loop built around the Virtual Reference Airgap is as effective as one built around a Reference Airgap.

It shall now be reminded that the just described Virtual Reference Airgap approach, being applicable to output functions symmetrical with respect to 180° (examples are sinusoidal and symmetric triangular functions), whenever it is necessary to resolve the already described—180° to 0° and 0° to +180° ambiguity requires a third magnetic field probe, H3, located at a third angular position (typically 90°) with respect to H1 and H2. Alternatively, for a most accurate compensation, said third magnetic field probe could be replaced by a second couple of diametrically opposed probes. Of course, for proper compensation also sensor H3 will need to be supplied by the same supply current as H1 and H2, and in FIG. 3 e it will hence appear connected in series to both them (or in parallel for magnetic field probes ratiometric to the supply voltage). If a second couple of diametrically opposed probes is instead used, then it can be supplied in the same way but on its own, independently from the supply of the first couple of probes.

It is considered a trivial task to adapt the airgap configurations depicted in FIGS. 2 b through 2 f to the Virtual Reference Airgap approach: just suppress one of the two airgaps, and move the corresponding magnetic field sensor to the other airgap, at an angular position diametrically opposed to the position of the other sensor.

For those applications where accuracy can be sacrificed in favour of simplicity of design, and hence reliability, the extremely simple circuit shown in FIG. 3 f represents an interesting alternative. R(B1) and R(B2) are two simple magnetoresistors (functions of B) connected as a resistive divider. The output voltage is hence

v _(o)=V/(1=R(B1)/R(B2))  (8)

which is NOT a linear function of the “B1/B2 Ratio”, especially when taking into account also the strongly non-linear form of R(B) as a function of B. However, by a suitable choice of the geometric parameters defining the form of said “B1/B2 Ratio”, even in this case it is possible to largely compensate for such non linearities. An example is shown in FIG. 4 a, whereby the “B1/B2 Ratio” is purposely designed to be a non-linear function of the angular displacement (between 0 and 180 degrees in FIG. 4 a), and whose deviation from linearity can be judged by comparing the B1/B2 curve with the ideally linear behaviour (the dotted line) shown for reference only.

FIG. 4 b shows an application example with two N-type magnetoresistors from Siemens, utilised in the range 0.3 T to 0.6 T, demonstrating how such a simple resistive divider circuit can nevertheless directly generate an output voltage linearly decreasing from 5V to 3V (or, for the symmetric case, linearly increasing from 3V to 5V), while maintaining the maximum deviation from linearity to within −0.4% to +0.1% @ 25° C., 0% to +0.6% @ 60° C., −1% to +0% @ −20° C.

For all the sensor configurations depicted in FIGS. 2 a through 2 f most of the magnetic flux generated by the permanent magnet is closed radially through the shaft (the arrows describe the main path followed by the magnetic flux, leakage paths are not represented). There are however instances where it is instead desirable to have most of the magnetic flux closing radially through an external cylindrical path, rather than through the shaft. Examples are those applications requiring a hollow shaft so that too small a cross-section would be available for closing the flux without magnetic saturation effects, or applications where it is desirable to better screen the magnetic field probes against the presence of magnetic fields external to the sensor. FIG. 4 c represents a cross-section (to aid understanding, FIG. 4 d depicts a perspective view of the same section) of an example of just such a configuration, and which is equivalent to that of FIG. 2 a, the difference being that now the magnetic flux is closed through the external cylindrical wall, and that the Variable Airgap is obtained by varying the thickness of ring D1, rather than the width of D2 a as it was the case in FIG. 2 a. Ring D2 serves the purpose to render as uniform as possible the magnetic field measured by H2 (or MR2) in the Reference Airgap. All the parts of this rotary magnetic circuit are fixed relatively to the central shaft (a non magnetic spacer fixing D2 to the shaft is omitted for clarity). FIGS. 4 e and 4 f depict the same configuration as in FIGS. 4 c and 4 d, but after suppressing the Reference Airgap, and relocating H2 to the Variable Airgap at an angular position diametrically opposed to H1. The Reference Airgap is then replaced by the Virtual Reference Airgap, built by taking the mean value of the B values measured by H1 and H2. For clarity, FIG. 4 e does not show the third magnetic field probe (or alternatively the second couple of probes) used to resolve the −180° to 0° and 0° to +180° ambiguity.

FIGS. 5 a and 5 b describe a configuration convenient for those applications where it might be desirable to mount the magnetic field probes parallel to the central shaft, rather than perpendicularly to it. H1 is located in the Reference Airgap, whereas H2 is located in a Variable Airgap obtained by varying the radial width of ring D2 as a function of angular position. The Virtual Reference Airgap version of this last configuration is depicted in FIGS. 5 c and 5 d. For clarity, FIG. 5 c does not show the third magnetic field probe (or alternatively the second couple of probes) used to resolve the −180° to 0° and 0° to +180° ambiguity.

Concerning the parallel magnetic circuit configuration of FIG. 1 b, for some applications it might be convenient to adopt a geometry such that the magnetic field probes H1 and H2 are located in airgaps of constant geometry, as to minimise cross-talk effects and non-linearities resulting from leakage flux and border effects whose impact would otherwise also vary with position. The task of varying the overall reluctance of a parallel branch of the magnetic circuit is then transferred to a third airgap of variable geometry, which can now be optimised free from the constraints imposed by the need to reserve some space for mounting a magnetic field probe. FIG. 1 e schematically represents such an approach, whereby the airgaps surrounding H1 and H2 are now of a constant geometry, while the task of varying the reluctance of the parallel branch crossed by flux φ2, is now delegated to a specialised variable airgap, V_(gap), whose geometry is designed to vary with position in such a way the “B1/B2 Ratio” corresponds to the desired function of position.

An interesting application of such an approach is the measurement of small relative angular displacements of two rotating elements, such as for example in torque sensors. A very common way to measure torque consists in measuring the relative angular displacement of two shafts coaxially connected by a torsion bar. FIG. 5 e depicts the cross section of a rotary magnetic circuit configuration optimised for just this type of measurements, while FIG. 5 f illustrates its perspective view, which helps in understanding the radial paths followed by the magnetic flux generated by the permanent magnet. The principle of operation is as follows:

-   -   the permanent magnet, PM, is radially magnetised, and it         generates a magnetic flux that then splits into two parallel         branches: φ1 and φ2;     -   the variable gap, V_(gap), of FIG. 1 e is in this case of a         circular design, and it is realised by means of a crown, C1,         featuring a plurality of teeth, and which can rotate relatively         to the corresponding teeth machined on part C2, so that a small         relative angular displacement between C1 and C2 will result in a         variation of the overall reluctance of the parallel branch         crossed by φ1;     -   all parts, except C1, are fixed to C2 by means of suitable         non-magnetic spacers (not shown for clarity), and they will         hence rotate together with C2, this in order to minimise effects         resulting from eddy currents which would be induced at high         speed operation, but it otherwise does not need to be so for low         speed applications;     -   ring D1 closes the path for flux φ1 making also sure that the B         value measured by H2 is as uniform as possible along the         corresponding circumference, as it is the case for the B value         measured by H1;     -   H1 and H2 are not rotating, but they are fixed to the external         printed circuit board featuring the signal conditioning and         processing electronics;     -   when C1 and C2 both rotate at the same angular rate, and without         any relative angular displacement, then the “B1/B2 Ratio” will         correspond to a well defined value, independent from the         absolute angular position along the full 360° arc;     -   when C1 and C2 still rotate at the same angular rate, but now         with some amount of relative angular displacement, then the         “B1/B2 Ratio” will still correspond to a well defined value,         which will still be independent from the absolute angular         position along the full 360° arc, but now such well defined         value will be different from the one measured at zero relative         angular displacement;     -   for torque measurement applications crown C1 would typically be         coupled to a first shaft, while C2 to a second shaft coaxial         with the first one, and said two shafts will then be coupled by         means of a torsion bar calibrated to yield a relative angular         displacement (just few degrees, typically) function of the         applied torque.

The inventive step of this invention shall be understood as independent from any detailed choice of the geometry defining the form of the “B1/B2 Ratio” function, rather it consists in the more general idea of arranging the geometry of a magnetic circuit in such a way that the measurement of angular (or linear) displacements can be carried out by computing the ratio between magnetic field values measured at two different locations, making it hence largely independent from variations in temperature or from drifts in the working point of the permanent magnet. It shall be appreciated that those skilled in the art, building on the features of the invention described above, now could easily imagine many changes, modifications, and-or substitutions. The following claims are intended to cover such changes as fall within the scope of the inventive step detailed in the above description. 

1. A contactless method to measure angular or linear displacements by computing the ratio between the output signals of two magnetic field sensors placed at two different locations of a magnetic circuit; characterised in that said method is arranged for using two magnetic field sensors to measure the value of the magnetic fields, B1 and B2, in two different airgaps of the same magnetic circuit, whereby the geometry of said magnetic circuit is designed to convert the displacement to be measured into a corresponding variation of the ratio between the output signals of said two magnetic field sensors; computing by means of electronic circuitry the ratio between the output signals of said two magnetic field sensor.
 2. Apparatus implementing the method described in claim 1, comprising: a magnetic circuit composed of a stationary part characterised by two airgaps located in two parallel branches of it and by a rotating ring moving relatively to the stationary part as exemplified in FIGS. 1 a and 1 b, a biasing permanent magnet, two stationary magnetic fields sensors, such as for example of the types based on the Hall effect or on the magnetoresistive effect, and a suitable electronic circuitry; characterised in that the geometry of said magnetic circuit is designed to vary, relatively to the locations of said two magnetic field sensors, as a function of the displacement to be measured; for the measurement of angular displacements said relative variation of geometry is obtained by means of the rotation of said ring of ferromagnetic material, whose radial cross-section geometrical parameters are further designed to vary along its circumference in such a way as to result in a variation of said magnetic field values such that the “B1/B2 Ratio” is a well defined function of said angular displacement; for the measurement of linear displacements said relative variation of geometry is obtained by means of the displacement of a bar of ferromagnetic material, whose transversal cross-section geometrical parameters are further designed to vary along its length in such a way as to result in a variation of said magnetic field values such that the “B1/B2 Ratio” is a well defined function of said linear displacement; a suitable electronic circuitry, such as for example of the well known analog divider type or of the microcontroller based type, is used to compute the ratio between the output signals of said magnetic field sensors, and hence generating an output voltage proportional to the “B1/B2 Ratio”.
 3. Apparatus as claimed in claim 2; characterised in that the two airgaps are located in the same branch of the magnetic circuit, as shown for example in FIGS. 1 c and 1 d, in such a way that they are both crossed by the same magnetic flux, and the ring (or bar) of ferromagnetic material is shaped with a geometry that varies along its circumference (or length) in such a way that the “B1/B2 Ratio” is a well defined function of the displacement to be measured;
 4. Apparatus implementing the method described in claim 1, comprising: a rotating magnetic circuit assembly composed by ring shaped parts surrounding a central cylindrical column and which is characterised by two airgaps whose relative radial cross-section geometries vary along the circumference as exemplified in FIGS. 2 a-2 b-2 c, a ring shaped permanent magnet rotating with said magnetic circuit, two stationary magnetic fields sensors, such as for example of the types based on the Hall effect or on the magnetoresistive effect, and a suitable electronic circuitry; characterised in that at the locations of said magnetic field sensors, said relative radial cross-sections geometries are designed to vary with the rotation of said rotating magnetic circuit assembly as a function of the angular displacement to be measured; said relative variation of radial cross-sections geometries is further designed to result in a variation of the magnetic field values measured by said two magnetic field sensors such that the “B1/B2 Ratio” is a well defined function of said angular displacement; a suitable electronic circuitry, such as for example of the well known analog divider type or of the microcontroller based type, is used to compute the ratio between the output signals of said magnetic field sensors, and hence generating an output voltage proportional to the “B1/B2 Ratio”.
 5. Apparatus as claimed in claim 4; characterised in that the permanent magnet is shaped as a cylindrical bar, which might also be of a hollow type, placed along the central axis as in the example of FIG. 2 d;
 6. Apparatus as claimed in claim 4; characterised in that the ring shaped permanent magnet is of a radially magnetised type, as in the examples of FIGS. 2 e and 2 f;
 7. Apparatus as claimed in claims 4, 5, 6; characterised in that the rotating assembly configurations of claims 4, 5, 6, are trivially modified by ideally cutting through a radial section to then ideally straighten the resulting cut rings into bars, so as to obtain configurations suitable for the measurement of linear displacements;
 8. Apparatus as claimed in claims 2, 3, 4, 5, 6, 7; characterised in that an output voltage proportional to the “B1/B2 Ratio” is generated directly at the output of one of the two magnetic field sensors, thanks to a feedback loop arranged to control the biasing current or the supply voltage common to both sensors, in such a way the equilibrium working point of said feedback loop corresponds to an output voltage for the other sensor equal to a well defined reference voltage, as schematically exemplified in FIGS. 3 c and 3 d;
 9. Apparatus as claimed in claims 2, 3, 4, 5, 6, 7; characterised in that the two magnetic field sensors are two simple magnetoresistors connected in a conventional resistive voltage divider configuration, as in the example of FIG. 3 f, whose output voltage V/(1+R(B1)/R(B2)) is consequently no longer a linear function of the “B1/B2 Ratio”, but that it can nevertheless be made to be a desired function of angular, or linear, displacement by arranging the magnetic circuit geometry in such a way that the “B1/B2 Ratio” is also a non-linear function of the displacement, as for example the function depicted in FIG. 4 a, carefully shaped to compensate, as far as possible, for the inherent non-linearities of the V/(1+R(B1)/R(B2)) output voltage of said resistive voltage divider;
 10. Apparatus implementing the method described in claim 1, comprising: a rotating magnetic circuit assembly composed by ring shaped parts surrounding a central shaft and surrounded by an external cylindrical tube serving the purpose to provide an outer path for the radial closing of the magnetic flux, and which is characterised by two airgaps whose relative radial cross-section geometries vary along the circumference, as exemplified in FIGS. 4 c-4 d by a ring of varying thickness, a ring shaped permanent magnet rotating with said magnetic circuit, two stationary magnetic fields sensors, such as for example of the types based on the Hall effect or on the magnetoresistive effect, and a suitable electronic circuitry; characterised in that at the locations of said magnetic field sensors, said relative radial cross-sections geometries are designed to vary with the rotation of said rotating magnetic circuit assembly as a function of the angular displacement to be measured; said relative variation of radial cross-sections geometries is further designed to result in a variation of the magnetic field values measured by said two magnetic field sensors such that the “B1/B2 Ratio” is a well defined function of said angular displacement; a suitable electronic circuitry, such as for example of the well known analog divider type or of the microcontroller based type, or of the feedback loop type described in claim 8, is used to compute the ratio between the output signals of said magnetic field sensors, and hence generating an output voltage proportional to the “B1/B2 Ratio”;
 11. Apparatus as claimed in claim 10; characterised in that the Reference Airgap is suppressed, and the corresponding magnetic field sensor H2 is relocated in the Variable Airgap, at an angular position diametrically opposed to the other sensor H1, as in the example of FIGS. 4 e and 4 f; the signals generated by H1 and H2 are then combined to reconstruct a Virtual Reference Airgap by computing a signal proportional to the mean value, Bvirtual=(B1+B2)/2, of the B values measured by H1 and H2; said signal proportional to Bvirtual is then used in a feedback loop arranged to control the biasing current or the supply voltage common to all sensors, in such a way that the equilibrium working point of said feedback loop corresponds to a Virtual Reference Airgap output voltage held constant to a value defined by a reference voltage, as in the example of FIG. 3 e, so that the output voltage of sensor H1 becomes proportional to the “B1/Bvirtual Ratio”; for those applications requiring to resolve the −180°/0° and 0°/+180° ambiguity, a third magnetic field probe supplied by the same biasing current or supply voltage common to all sensors, or alternatively a second couple of probes, is then added at a different angular position along the Variable Airgap;
 12. Apparatus as claimed in claim 10; characterised in that the ring shaped ferromagnetic parts and permanent magnet are arranged as to allow the mounting of the magnetic field sensors with their main axis parallel to the axis of the central shaft, as exemplified in FIGS. 5 a and 5 b;
 13. Apparatus as claimed in claim 12; characterised in that the Reference Airgap is suppressed, and the corresponding magnetic field sensor H2 is relocated in the Variable Airgap, at an angular position diametrically opposed to the other sensor H1, as in the example of FIGS. 5 c and 5 d; the signals generated by H1 and H2 are then combined to reconstruct a Virtual Reference Airgap by computing a signal proportional to the mean value, Bvirtual=(B1+B2)/2, of the B values measured by H1 and H2; said signal proportional to Bvirtual is then used in a feedback loop arranged to control the biasing current or the supply voltage common to all sensors, in such a way that the equilibrium working point of said feedback loop corresponds to a Virtual Reference Airgap output voltage held constant to a value defined by a reference voltage, as in the example of FIG. 3 e, so that the output voltage of sensor H1 becomes proportional to the “B1/Bvirtual Ratio”; for those applications requiring to resolve the −180°/0° and 0°/+180° ambiguity, a third magnetic field probe supplied by the same biasing current or supply voltage common to all sensors, or alternatively a second couple of probes, is then added at a different angular position along the Variable Airgap;
 14. Apparatus implementing the method described in claim 1, comprising: a rotating magnetic circuit assembly biased by a ring shaped radially magnetised permanent magnet, and composed by two radial parallel branches, one of which features an airgap of uniform circular geometry, while the other features two airgaps, with one airgap being of uniform circular geometry and the other of a variable geometry function of the relative angular displacement with respect to a second independently rotating element, and of which an illustrative example is depicted in FIGS. 5 e and 5 f, further arranged to make use of two stationary magnetic fields sensors, such as for example of the types based on the Hall effect or on the magnetoresistive effect, in order to measure the value of the magnetic field in said two airgaps of uniform circular geometry; characterised in that the airgap of variable geometry is designed to result in a variation of the magnetic field values measured by said two magnetic field sensors such that the “B1/B2 Ratio” is a well defined function of said relative angular displacement, independent from the value of any absolute angular displacement; a suitable electronic circuitry, such as for example of the well known analog divider type or of the microcontroller based type, or of the feedback loop type described in claim 8, is used to compute the ratio between the output signals of said magnetic field sensors, and hence generating an output voltage proportional to the “B1/B2 Ratio”; by further coaxially coupling said rotating magnetic circuit to a first shaft, and coaxially coupling said second independently rotating element to a second shaft, in turn coaxially coupled to the first shaft by means of a calibrated torsion bar, allows the realisation of a simple and robust torque sensor. 